Seeding approach to nucleation in the NVT ensemble: The case of bubble cavitation in overstretched Lennard Jones fluids.

Simulations are widely used to study nucleation in first order phase transitions due to the fact that they have access to the relevant length and time scales. However, simulations face the problem that nucleation is an activated process. Therefore, rare event simulation techniques are needed to promote the formation of the critical nucleus. The Seeding method, where the simulations are started with the nucleus already formed, has proven quite useful in efficiently providing estimates of the nucleation rate for a wide range of orders of magnitude. So far, Seeding has been employed in the NPT ensemble, where the nucleus either grows or redissolves. Thus, several trajectories have to be run in order to find the thermodynamic conditions that make the seeded nucleus critical. Moreover, the nucleus lifetime is short and the statistics for obtaining its properties is consequently poor. To deal with these shortcomings we extend the Seeding method to the NVT ensemble. We focus on the problem of bubble nucleation in a metastable Lennard Jones fluid. We show that, in the NVT ensemble, it is possible to equilibrate and stabilise critical bubbles for a long time. The nucleation rate inferred from NVT-Seeding is fully consistent with that coming from NPT-Seeding. The former is quite suitable to obtain the nucleation rate along isotherms, whereas the latter is preferable if the dependence of the rate with temperature at constant pressure is required. Care should be taken with finite size effects when using NVT-Seeding. Further work is required to extend NVT seeding to other sorts of phase transitions.

Seeding approach to bubble nucleation in superheated Lennard-Jones fluids.

We investigate vapor homogeneous nucleation in a superheated Lennard-Jones liquid with computer simulations. Special simulation techniques are required to address this study since the nucleation of a critical vapor bubble-one that has an equal chance to grow or shrink-in a moderately superheated liquid is a rare event. We use the Seeding method, which combines Classical Nucleation Theory with computer simulations of a liquid containing a vapor bubble to provide bubble nucleation rates in a wide temperature range. Seeding has been successfully applied to investigate the nucleation of crystals in supercooled fluids, and here we apply it to the liquid-to-vapor transition. We find that the Seeding method provides nucleation rates that are consistent with independent calculations not based on the assumptions of Classical Nucleation Theory. Different criteria to determine the radius of the critical bubble give different rate values. The accuracy of each criterion depends of the degree of superheating. Moreover, seeding simulations show that the surface tension depends on pressure for a given temperature. Therefore, using Classical Nucleation Theory with the coexistence surface tension does not provide good estimates of the nucleation rate.

Molecular dynamics study of nanoconfined TIP4P/2005 water: how confinement and temperature affect diffusion and viscosity.

In the past few decades great effort has been devoted to the study of water confined in hydrophobic geometries at the nanoscale (tubes and slit pores) due to the multiple technological applications of such systems, ranging from drug delivery to water desalination devices. To our knowledge, neither numerical/theoretical nor experimental approaches have so far reached a consensual understanding of structural and transport properties of water under these conditions. In this work, we present molecular dynamics simulations of TIP4P/2005 water under different nanoconfinements (slit pores or nanotubes, with two degrees of hydrophobicity) within a wide temperature range. It has been found that water is more structured near the less hydrophobic walls, independently of the confining geometries. Meanwhile, we observe an enhanced diffusion coefficient of water in both hydrophobic nanotubes. Finally, we propose a confined Stokes-Einstein relation to obtain the viscosity from diffusivity, whose result strongly differs from the Green-Kubo expression that has been used in previous works. While viscosity computed with the Green-Kubo formula (applied for anisotropic and confined systems) strongly differs from that of the bulk, viscosity computed with the confined Stokes-Einstein relation is not so much affected by the confinement, independently of its geometry. We discuss the shortcomings of both approaches, which could explain this discrepancy.

Pressure control in interfacial systems: Atomistic simulations of vapor nucleation.

A large number of phenomena of scientific and technological interest involve multiple phases and occur at constant pressure of one of the two phases, e.g., the liquid phase in vapor nucleation. It is therefore of great interest to be able to reproduce such conditions in atomistic simulations. Here we study how popular barostats, originally devised for homogeneous systems, behave when applied straightforwardly to heterogeneous systems. We focus on vapor nucleation from a super-heated Lennard-Jones liquid, studied via hybrid restrained Monte Carlo simulations. The results show a departure from the trends predicted for the case of constant liquid pressure, i.e., from the conditions of classical nucleation theory. Artifacts deriving from standard (global) barostats are shown to depend on the size of the simulation box. In particular, for Lennard-Jones liquid systems of 7000 and 13 500 atoms, at conditions typically found in the literature, we have estimated an error of 10-15 kBT on the free-energy barrier, corresponding to an error of 104-106 s-1σ-3 on the nucleation rate. A mechanical (local) barostat is proposed which heals the artifacts for the considered case of vapor nucleation.

Micro-phase separation in two dimensional suspensions of self-propelled spheres and dumbbells.

We use numerical simulations to study the phase behavior of self-propelled spherical and dumbbellar particles interacting via micro-phase separation inducing potentials. Our results indicate that under the appropriate conditions, it is possible to drive the formation of two new active states; a spinning cluster crystal, i.e. an ordered mesoscopic phase having finite size spinning crystallites as lattice sites, and a fluid of living clusters, i.e. a two dimensional fluid where each "particle" is a finite size living cluster. We discuss the dynamics of these phases and suggest ways of extending their stability under a wide range of active forces.

On the time required to freeze water.

By using the seeding technique the nucleation rate for the formation of ice at room pressure will be estimated for the TIP4P/ICE model using longer runs and a smaller grid of temperatures than in the previous work. The growth rate of ice will be determined for TIP4P/ICE and for the mW model of water. Although TIP4P/ICE and mW have a similar melting point and melting enthalpy, they differ significantly in the dynamics of freezing. The nucleation rate of mW is lower than that of TIP4P/ICE due to its higher interfacial free energy. Experimental results for the nucleation rate of ice are between the predictions of these two models when obtained from the seeding technique, although closer to the predictions of TIP4P/ICE. The growth rate of ice for the mW model is four orders of magnitude larger than for TIP4P/ICE. Avrami's expression is used to estimate the crystallization time from the values of the nucleation and growth rates. For mW the minimum in the crystallization time is found at approximately 85 K below the melting point and its value is of about a few ns, in agreement with the results obtained from brute force simulations by Moore and Molinero. For the TIP4P/ICE the minimum is found at about 55 K below the melting point, but its value is about ten microseconds. This value is compatible with the minimum cooling rate required to avoid the formation of ice and obtaining a glass phase. The crossover from the nucleation controlled crystallization to the growth controlled crystallization will be discussed for systems of finite size. This crossover could explain the apparent discrepancy between the values of J obtained by different experimental groups for temperatures below 230 K and should be considered as an alternative hypothesis to the two previously suggested: internal pressure and/or surface freezing effects. A maximum in the compressibility was found for the TIP4P/ICE model in supercooled water. The relaxation time is much smaller than the crystallization time at the temperature at which this maximum occurs, so this maximum is a real thermodynamic feature of the model. At the temperature of minimum crystallization time, the crystallization time is larger than the relaxation time by just two orders of magnitude.

Anomalous dynamics of an elastic membrane in an active fluid.

Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multifolded states, whereas stiff membranes fluctuate between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mechanical work at the microscale.

The role of particle shape in active depletion.

Using numerical simulations, we study how a solution of small active disks, acting as depletants, induces effective interactions on large passive colloids. Specifically, we analyze how the range, strength, and sign of these interactions are crucially dependent on the shape of the colloids. Our findings indicate that while colloidal rods experience a long-ranged predominantly attractive interaction, colloidal disks feel a repulsive force that is short-ranged in nature and grows in strength with the size ratio between the colloids and active depletants. For colloidal rods, simple scaling arguments are proposed to characterize the strength of these induced interactions.

Homogeneous ice nucleation evaluated for several water models.

In this work, we evaluate by means of computer simulations the rate for ice homogeneous nucleation for several water models such as TIP4P, TIP4P/2005,TIP4P/ICE, and mW (following the same procedure as in Sanz et al. [J. Am. Chem. Soc. 135, 15008 (2013)]) in a broad temperature range. We estimate the ice-liquid interfacial free-energy, and conclude that for all water models γ decreases as the temperature decreases. Extrapolating our results to the melting temperature, we obtain a value of the interfacial free-energy between 25 and 32 mN/m in reasonable agreement with the reported experimental values. Moreover, we observe that the values of γ depend on the chosen water model and this is a key factor when numerically evaluating nucleation rates, given that the kinetic prefactor is quite similar for all water models with the exception of the mW (due to the absence of hydrogens). Somewhat surprisingly the estimates of the nucleation rates found in this work for TIP4P/2005 are slightly higher than those of the mW model, even though the former has explicit hydrogens. Our results suggest that it may be possible to observe in computer simulations spontaneous crystallization of TIP4P/2005 at about 60 K below the melting point.

Exposing a dynamical signature of the freezing transition through the sound propagation gap.

The conventional view of freezing holds that nuclei of the crystal phase form in the metastable fluid through purely stochastic thermal density fluctuations. The possibility of a change in the character of the fluctuations as the freezing point is traversed is beyond the scope of this perspective. Here we show that this perspective may be incomplete by examination of the time autocorrelation function of the longitudinal current, computed by molecular dynamics for the hard-sphere fluid around its freezing point. In the spatial window where sound is overdamped, we identify a change in the long-time decay of the correlation function at the known freezing points of monodisperse and moderately polydisperse systems. The fact that these findings agree with previous experimental studies of colloidal systems in which particle are subject to diffusive dynamics, suggests that the dynamical signature we identify with the freezing transition is a consequence of packing effects alone.

Anomalous thermomechanical properties of a self-propelled colloidal fluid.

We use numerical simulations to compute the equation of state of a suspension of spherical self-propelled nanoparticles in two and three dimensions. We study in detail the effect of excluded volume interactions and confinement as a function of the system's temperature, concentration, and strength of the propulsion. We find a striking nonmonotonic dependence of the pressure on the temperature and provide simple scaling arguments to predict and explain the occurrence of such anomalous behavior. We explicitly show how our results have important implications for the effective forces on passive components suspended in a bath of active particles.

Nucleation free-energy barriers with Hybrid Monte-Carlo/Umbrella Sampling.

The aim of this work is to evaluate nucleation free-energy barriers using molecular dynamics (MD). More specifically, we use a combination of Hybrid Monte Carlo (HMC) and an Umbrella Sampling scheme, and compute the crystallisation barrier of NaCl from its melt. Firstly the convergence and performance of HMC for different time-steps and the number of MD steps within a HMC cycle are assessed. The calculated potential energies and densities converge regardless of the chosen time-step. However the acceptance ratio of the Metropolis step within the HMC scheme strongly depends on the time-step and affects the performance. It is shown that the acceptance ratio is close to 100% for time-steps of the order of those commonly used in molecular dynamics runs. We then explore the results obtained with a "non-Metropolised" version of HMC where the MD trajectories are always accepted (omitting the Metropolis criteria) and conclude that they are satisfactory for time-steps below 5 fs. Next, HMC is combined with Umbrella Sampling (HMC/US) to compute the nucleation free-energy for both the standard and the "non-Metropolised" HMC (using a small time-step) and in both cases find excellent agreement with the reported values. To conclude, we explore approximations to the HMC/US technique implementing HMC with isothermal-isobaric MD trajectories. The computed nucleation free-energy curve is coincident, within the statistical error, with previous calculations.

Curvature-induced activation of a passive tracer in an active bath.

We use numerical simulations to study the motion of a large asymmetric tracer immersed in a low-density suspension of self-propelled particles in two dimensions. Specifically, we analyze how the curvature of the tracer affects its translational and rotational motion in an active environment. We find that even very small amounts of curvature are sufficient for the active bath to impart directed motion to the tracer, which results in its effective activation. We propose simple scaling arguments to characterize this induced activity in terms of the curvature of the tracer and the strength of the self-propelling force. Our results suggest new ways of controlling the transport properties of passive tracers in an active medium by carefully tailoring their geometry.

Chemotactic clusters in confined run-and-tumble bacteria: a numerical investigation.

We present a simulation study of pattern formation in an ensemble of chemotactic run-and-tumble bacteria, focussing on the effect of spatial confinement, either within traps or inside a maze. These geometries are inspired by previous experiments probing pattern formation in chemotactic strains of E. coli under these conditions. Our main result is that a microscopic model of chemotactic run-and-tumble particles which themselves secrete a chemoattractant is able to reproduce the main experimental observations, namely the formation of bacterial aggregates within traps and in dead ends of a maze. Our simulations also demonstrate that stochasticity plays a key role and leads to a hysteretic response when the chemotactic sensitivity is varied. We compare the results of run-and-tumble particles with simulations performed with a simplified version of the model where the active particles are smooth swimmers which respond to chemotactic gradients by rotating towards the source of chemoattractant. This class of models leads again to aggregation, but with quantitative and qualitative differences in, for instance, the size and shape of clusters.

Activity-induced collapse and reexpansion of rigid polymers.

We study the elastic properties of a rigid filament in a bath of self-propelled particles. We find that while fully flexible filaments swell monotonically upon increasing the strength of the propelling force, rigid filaments soften for moderate activities, collapse into metastable hairpins for intermediate strengths, and eventually reexpand when the strength of the activity of the surrounding fluid is large. This collapse and reexpansion of the filament with the bath activity is reminiscent of the behavior observed in polyelectrolytes in the presence of different concentrations of multivalent salt.

Homogeneous ice nucleation at moderate supercooling from molecular simulation.

Among all of the freezing transitions, that of water into ice is probably the most relevant to biology, physics, geology, or atmospheric science. In this work, we investigate homogeneous ice nucleation by means of computer simulations. We evaluate the size of the critical cluster and the nucleation rate for temperatures ranging between 15 and 35 K below melting. We use the TIP4P/2005 and the TIP4P/ice water models. Both give similar results when compared at the same temperature difference with the model's melting temperature. The size of the critical cluster varies from ∼8000 molecules (radius = 4 nm) at 15 K below melting to ∼600 molecules (radius = 1.7 nm) at 35 K below melting. We use Classical Nucleation Theory (CNT) to estimate the ice-water interfacial free energy and the nucleation free-energy barrier. We obtain an interfacial free energy of 29(3) mN/m from an extrapolation of our results to the melting temperature. This value is in good agreement both with experimental measurements and with previous estimates from computer simulations of TIP4P-like models. Moreover, we obtain estimates of the nucleation rate from simulations of the critical cluster at the barrier top. The values we get for both models agree within statistical error with experimental measurements. At temperatures higher than 20 K below melting, we get nucleation rates slower than the appearance of a critical cluster in all water of the hydrosphere during the age of the universe. Therefore, our simulations predict that water freezing above this temperature must necessarily be heterogeneous.

Free energy calculations for molecular solids using GROMACS.

In this work, we describe a procedure to evaluate the free energy of molecular solids with the GROMACS molecular dynamics package. The free energy is calculated using the Einstein molecule method that can be regarded as a small modification of the Einstein crystal method. Here, the position and orientation of the molecules is fixed by using an Einstein field that binds with harmonic springs at least three non-collinear atoms (or points of the molecule) to their reference positions. The validity of the Einstein field is tested by performing free-energy calculations of methanol, water (ice), and patchy colloids molecular solids. The free energies calculated with GROMACS show a very good agreement with those obtained using Monte Carlo and with previously published results.

Homogeneous bubble nucleation in water at negative pressure: a Voronoi polyhedra analysis.

We investigate vapor bubble nucleation in metastable TIP4P/2005 water at negative pressure via the Mean First Passage Time (MFPT) technique using the volume of the largest bubble as a local order parameter. We identify the bubbles in the system by means of a Voronoi-based analysis of the molecular dynamics trajectories. By comparing the features of the tessellation of liquid water at ambient conditions to those of the same system with an empty cavity we are able to discriminate vapor (or interfacial) molecules from the bulk ones. This information is used to follow the time evolution of the largest bubble until the system cavitates at 280 K above and below the spinodal line. At the pressure above the spinodal line, the MFPT curve shows the expected shape for a moderately metastable liquid from which we estimate the bubble nucleation rate and the size of the critical cluster. The nucleation rate estimated using Classical Nucleation Theory turns out to be about 8 order of magnitude lower than the one we compute by means of MFPT. The behavior at the pressure below the spinodal line, where the liquid is thermodynamically unstable, is remarkably different, the MFPT curve being a monotonous function without any inflection point.

Living clusters and crystals from low-density suspensions of active colloids.

Recent studies aimed at investigating artificial analogs of bacterial colonies have shown that low-density suspensions of self-propelled particles confined in two dimensions can assemble into finite aggregates that merge and split, but have a typical size that remains constant (living clusters). In this Letter, we address the problem of the formation of living clusters and crystals of active particles in three dimensions. We study two systems: self-propelled particles interacting via a generic attractive potential and colloids that can move toward each other as a result of active agents (e.g., by molecular motors). In both cases, fluidlike "living" clusters form. We explain this general feature in terms of the balance between active forces and regression to thermodynamic equilibrium. This balance can be quantified in terms of a dimensionless number that allows us to collapse the observed clustering behavior onto a universal curve. We also discuss how active motion affects the kinetics of crystal formation.